NCSS 2000 is a comprehensive, easy-to-use, statistical program. It is…• Comprehensive and accurate.

Includes over 200 procedures andgraphics.

• Easy to learn and use.• Windows 9x/NT compatible.• Imports/ exports major spreadsheet,

database, and statistical file formats.• Year 2000 Compliant.• Output mixes text and graphics and is

easily transferred to wordprocessors.

• Processes large data files (over 1000variables and 200,000 rows).

Built-In Word ProcessorAll reports are displayed using our built-inword processor. You can quickly view, edit,save, and print your output. Reports are storedin the rich-text format that can be read bymost word processors, so you can easily saveNCSS reports for further use in Word. Theoutput document mixes text and graphstogether. The text portions of the reports areformatted using tabs (not spaces), so they areeasily reformatted.

Built-In SpreadsheetEntering data is simple using our MicrosoftExcel compatible spreadsheet. We import(and export) Lotus, Excel, dBase,Access, SAS, SPSS, Paradox, andASCII formats. So if your data is in anotherformat, chances are you can easily import itinto NCSS 2000.

System RequirementsRuns on Windows 9x, NT, and compatiblecomputers with at least 8 megs of RAM and30 megs of hard disk space.

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Curve FittingBuilt-In ModelsModel SearchingNonlinear RegressionRatio of PolynomialsUser-SpecifiedModelsMiscellaneousAppraisal Ratio StudiesArea Under CurveChi-Square TestConfidence LimitsCross TabulationData ScreeningFisher’s Exact TestFrequency DistributionsMantel-Haenszel TestNonparametric TestsNormality TestsProbability CalculatorProportion TestsTables of Means, Etc.Trimmed MeansUnivariate Statistics

Analysis of Variance and T-TestsAnalysis of CovarianceAnalysis of VarianceBarlett Variance TestFactorial Design AnalysisFriedman TestGeiser-Greenhouse CorrectionGeneral Linear ModelsMann-Whitney TestMANOVAMultiple Comparison TestsOne-Sample T-TestsOne-Way ANOVAPaired T-TestsPower CalculationsRepeated Measures ANOVATwo-Sample T-TestsWilcoxon Test

Plots and GraphsBar ChartsBox PlotsContour PlotDot PlotsError Bar ChartsHistogramsPercentile PlotsPie ChartsProbability PlotsROC CurvesScatter PlotsScatter Plot MatrixSurface PlotsViolin Plots

Regression / CorrelationAll-Possible SearchCanonical CorrelationCorrelation MatricesKendall’s Tau CorrelationLogistic RegressionMultiple RegressionNonlinear RegressionPC RegressionProportional-HazardsResponse-SurfaceRidge RegressionRobust RegressionStepwise RegressionSpearman CorrelationVariable Selection

Time Series AnalysisARIMA / Box - JenkinsDecompositionExponentialSmoothingHarmonic AnalysisHolt - WintersSeasonal AnalysisSpectral AnalysisTrend Analysis

Survival / ReliabilityAccelerated Life TestsCensoring - All TypesExponential FittingExtreme-Value FittingHazard RatesKaplan-MeierLognormal FittingLog-Rank TestsProbit AnalysisProportional-HazardsSurvival DistributionsWeibull AnalysisWeibull Regression

Experimental DesignsBalanced Inc. BlockBox-BehnkenCentral CompositeD-Optimal DesignsFractional FactorialLatin SquaresPlacket-BurmanResponse SurfaceScreeningTaguchi

Quality ControlXbar-R ChartC, P, NP, U ChartsCapability AnalysisCusum, EWMA ChartIndividuals ChartMoving Average ChartPareto ChartR & R Studies

Multivariate AnalysisClustering - KmeansClustering - HierarchicalCorrespondenceAnalysisDiscriminant AnalysisFactor AnalysisItem AnalysisItem Response AnalysisLoglinear ModelsMANOVAMulti-Way TablesMultidimensional ScalingPrincipal ComponentsNCSS Statistical Software • 329 North 1000 East • Kaysville, Utah 84037

Internet (download free demo version): http://www.ncss.com • Email: sales@ncss.comToll Free: (800) 898-6109 • Tel: (801) 546-0445 • Fax: (801) 546-3907

Trial Copy AvailableYou can try out the copy of NCSS 2000 onthe enclosed CD or download it from ourwebsite. This trial copy allows the analysis ofup to one hundred rows of data. It is good for30 days from the time you install the software.

NCSS 2000 – “Number Cruncher”Comprehensive, Easy to use, Statistical Software

NCSS provides and complete set of statistical charts and graphs. You control the labels, lines, andcolors of the graphs. The graphs may be copied to your favorite word processor or graphics editingpackage.

Sample Plots

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• Box plot• Chi-square probability plot• Density trace• Dot plot• Exponential probability plot• Frequency polygon• Gamma probability plot

• Grid plot• Half normal probability plot• Histogram• Normal probability plot• Percentile plot• Scatter plot• Scatter plot matrix

• Sunflower plot• Uniform probability plot• Violin plot• Weibull probability plot

Charts and Graphs

Several procedures are available for tabulating and summarizing your data. The frequency tableprocedure provides tabulation of single variables. The cross tabulation procedure provides tabulationof two variables into two-way tables. The descriptive tables procedure computes summary statistics(means, median, standard deviations, etc.) according to up to eight breakdown variables. All ofthese procedures provide numeric and graphic reports. A specialized appraisal ratio module providesreports for mass appraisal.

Frequency Table Report

Row Percentages SectionValues

Variables 0 0.5 1 2 3 TotalGarage Size 4.7 0.0 65.3 28.7 1.3 100.0Fireplaces 26.0 0.0 52.0 22.0 0.0 100.0Brick Ratio 34.0 31.3 34.7 0.0 0.0 100.0Total 21.6 10.4 50.7 16.9 0.4 100.0

Column Percentages SectionValues

Variables 0 0.5 1 2 3 TotalGarage Size 7.2 0.0 43.0 56.6 100.0 33.3Fireplaces 40.2 0.0 34.2 43.4 0.0 33.3Brick Ratio 52.6 100.0 22.8 0.0 0.0 33.3Total 100.0 100.0 100.0 100.0 100.0 100.0

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• Cross Tabulation• Armitage test for trend• Break Variables (up to five)• Chi-square test• Contingency analysis• Continuous variables allowed• Cramer’s V• Expected values• Fisher’s exact test• Gamma• Kendall’s tau - B & C• Lambda A & B• McNemar Test• Percentages• Phi coefficient• Text variables allowed• Tschuprow’s T• Value labels

• Descriptive Statistics• Average absolute deviation• Coef. of dispersion - COD• Coefficient of variation• Confidence limits• Density trace• Fisher’s g1 and g2• Geometric mean• Harmonic mean• Histogram• Kurtosis measures• Means, medians, modes• Mininmum and maximum• Normal probability plot• Normality tests• Percentiles• Price-related diff. - PRD• Skewness measures• Standard deviation / error• Stem-leaf plot• Trimmed mean

• Descriptive Tables• Numeric break variables• One-way and Two-way tables• Plots of tabulated statistics• Tables of medians, means,

standard deviations, counts,COV’s, and COD’s

• Text break variables• Value labels• Frequency Tables• Chi-square test• Counts• Cumulative statistics• Frequency distribution• Multinomial test• Percents

Descriptive Statistics and Cross Tabulation

Curve fitting refers to nonlinear-regression techniques for fitting curved lines to X-Y data. You canselect a standard model from the large list of precoded models or you can enter your own. If you donot have a specific model in mind, the program can search through hundreds of possible modelslooking for the one that best fits your data. The program will fit models with up to four independentvariables.

Model Estimation Section

Parameter Parameter Asymptotic Lower UpperName Estimate Standard Error 95% C.L. 95% C.L.A 0.3901402 5.033759E-03 0.3799816 0.4002987B 0.101633 1.336168E-02 7.466801E-02 0.1285979

Dependent YIndependent XModel Y = A+(0.49-A)*EXP(-B*(X-8))R-Squared 0.873375Iterations 13Estimated Model(.3901402)+(0.49-(.3901402))*EXP(-(.101633)*((X)-8))

Predicted Values and Residuals Section

Row Predicted Lower 95.0% Upper 95.0%No. X Y Value Value Value Residual1 8 0.49 0.49 0.4679772 0.5120228 02 8 0.49 0.49 0.4679772 0.5120228 03 10 0.48 0.4716319 0.4494232 0.4938406 0.00836814 10 0.47 0.4716319 0.4494232 0.4938406 -0.00163195 10 0.48 0.4716319 0.4494232 0.4938406 0.0083681

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• Bleasdale-Nelder Model• Double-Exponential Model• Exponential Model• Farazdaghi Model• Gompertz Models• Goodness of Fit Measures• Holliday Model• Logistic Model• Lognormal Model

• Marquart algorithm• Monomolecular Model• Morgan-Mercer Model• Nonlinear Regression• Normal Model• Piecewise-Polynomials• Probability Plots• Ratio of Polynomials• Reciprocal Model

• Richards Model• Scatter-Plot Matrix• Search Routines• Sum of Functions Regression• Transformation Bias

Correction• User-Supplied Models• Weibull Model

Curve Fitting

Regression analysis refers to a group of techniques for studying the relationships among two ormore variables. NCSS makes it easy to run either a simple linear regression analysis or a complexmultiple regression analysis. You can perform a regression analysis with modern graphical andnumeric residual analysis. Major options include multiple regression, stepwise regression, correlationmatrix, residual analysis, robust regression, all-possible regressions, response surface regression,proportional hazards regression, ridge regression, and logistic regression.

Multiple Regression ReportRegression Equation Section

Independent Regression Standard T-Value Prob Decision PowerVariable Coefficient Error (Ho: B=0) Level (5%) (5%)Intercept 85.24039 23.69514 3.5974 .005772 Reject Ho .891498Test1 -1.933571 1.029096 -1.8789 .092969 Accept Ho .389629Test2 -1.659881 .872896 -1.9016 .089661 Accept Ho .397357Test3 .1049543 .219902 .4773 .644541 Accept Ho .071290R-Squared .399068

Normality Tests SectionAssumption Value Probability Decision(5%)Skewness 2.0329 .042064 RejectedKurtosis 1.5798 .114144 AcceptedOmnibus 6.6285 .036361 Rejected

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• All-possible regressions• Alpha level is flexible• Beta coefficients• Biweight regression• Coefficient of variation• Condition number• Confidence limits• Cook’s D• Correlations• CovRatio• Cp Statistic• DFBetas• Dffits• Durbin Watson statistic• Eigenvalues• Eigenvectors• F-ratios• Hat diagonal• Inverse diagonal• LAV regression

• Logistic regression• Mean squares• Multiple regression• Multiple regression• Normal probability plot• Normality tests of residuals• Partial correlation• Pearson’s correlation• Power calculations• Predicted values• Prediction limits• Predicts new observations• Press statistic• P.C. Regression• Proportional-Hazards• R-bar squared• R-squared• Regression coefficient• Residual analysis and plots• Response surface analysis

• Ridge Regression• Robust regression• Rstudent• Serial correlation plot• Simple linear regression• Spearman’s rank correlation• Standard error of beta• Standardized coefficient• Stepwise regression• Sum of squares• T-test for beta=0• Through the origin• Tolerance level• Variable selection• Variance inflation factor• Weighted regression

Regression Analysis

The t-test procedures test the difference between two averages. The two sample t-test is used whenthe means come from two independent samples. The paired t-test is used when the observationsare obtained in pairs. The one sample t-test is used to compare a single mean with a target value.NCSS offers a comprehensive t-test analysis. It automatically checks all model assumptions,performs analogous nonparametric tests, displays appropriate plots, and computes confidence limits.

Two-Sample T-TestDescriptive Statistics Section

Standard Standard 95% LCL 95% UCLVariable Count Mean Deviation Error of Mean of MeanYldA 13 549.3846 168.7629 46.80641 447.4022 651.367YldB 16 557.5 104.6219 26.15546 501.7509 613.249

Confidence-Limits of Difference SectionVariance Mean Standard Standard 95% LCL 95% UCLAssumption DF Difference Deviation Error of Mean of MeanEqual 27 -8.115385 136.891 51.11428 -112.9932 96.76247Unequal 19.1690 -8.115385 198.5615 53.61855 -120.2734 104.0426

Equal-Variance T-Test SectionAlternative Prob Decision Power PowerHypothesis T-Value Level (5%) (Alpha=.05) (Alpha=.01)(YldA)-(YldB)<>0 -0.1588 0.875032 Accept Ho 0.052693 0.010837(YldA)-(YldB)<0 -0.1588 0.437516 Accept Ho 0.068110 0.014804(YldA)-(YldB)>0 -0.1588 0.562484 Accept Ho 0.035954 0.006616

Tests of Assumptions SectionAssumption Value Probability Decision(5%)Skewness Normality (YldA) 0.2691 0.787854 Cannot reject normalityKurtosis Normality (YldA) 0.3081 0.758028 Cannot reject normalityOmnibus Normality (YldA) 0.1673 0.919743 Cannot reject normalityVariance-Ratio Equal-Variance Test 2.6020 0.092546 Cannot reject equal variancesModified-Levene Equal-Variance Test 13.9235 0.002234 Reject equal variances

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• Aspin-Welch unequal-variancetest

• Box plots• Confidence limits• Descriptive statistics• Kolmogorov-Smirnov test• Levene equal-variance test

• Mann-Whitney U test• Normal probability plots• Normality tests• One and two tailed tests• One sample t-test• Pair comparisons t-test

• Power calculations• Probability levels• Quantile test• Two sample t-test• Unequal variance case• Wilcoxon rank sum test

T-Tests

Analysis of variance is the statistical technique for testing differences among group means. NCSScontains several analysis of variance procedures, including general linear models (GLM), one-wayanalysis of variance, unweighted means analysis of variance, and MANOVA. You can perform asimple one-way analysis of variance, a complex repeated-measures analysis of variance, a factorialanalysis of variance, an analysis of covariance, and a host of multiple-comparison tests. Allprocedures work with balanced and unbalanced experimental designs.

Analysis of Variance Table

Source Sum of Mean Prob PowerTerm DF Squares Square F-Ratio Level (Alpha=0.05)A (Treatment) 3 486.7488 165.5833 .61 .555761 .089834B(A) 15 4064.833 270.9889 C (Time) 1 277.7778 277.7778 50.51 .000004* .995231AC 3 352.0833 117.3611 21.34 .000041* .968851BC(A) 15 82.5 5.5

Tukey's HSD Multiple-Comparison TestTerm A: ExerciseAlpha=0.050 Error Term=B(A) DF=15 MSE=270.9889 Critical Value=4.895637

DifferentGroup Count Mean From Groups1 3 210.66674 3 211.33333 3 2382 3 257.6667

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• Analysis of covariance• ANOVA table• Area Under Curve• Assumptions testing• Automatic F-ratios• Bonferroni tests• Box plots• Box’s M test• Comparisons• Contrasts• Covariance analysis• Duncans test• Expected mean squares• F-ratios• Factorial designs• Fishers LSD test• Fixed terms• Fractional factorial designs• Geisser-Greenhouse• GLM solution

• Hotelling’s trace• Huynh-Feldt Correction• Interation plots• Kruskal Wallis z tests• Latin square designs• Least-squares means• Levene Variance test• MANOVA (with up to 10

factors)• Mauchley’s Test• Mean Squares• Means plots• Multiple comparisons of

factors• Multiple comparisons of

interactions• Nested terms• Newman-Keuls test• Normality tests• Pillai’s Trace

• Planned comparisions• Post-hoc tests• Power calculations• Random terms• Randomized complete block• Repeated measures• R and R Study• Roy’s Root• Scheffe’s test• Split-plot designs• Tukey-Kramer HSD tests• Unbalanced data• Wilks’ Lambda

Analysis of Variance

The repeated measures procedure performs an analysis of variance on within-subject designs usingthe general linear models approach. The experimental design may include up to three between-subject factors as well as three within-subject factors. Box’s M test and Mauchley’s test of theassumptions about the within-subject covariance matrices are provided. Geisser-Greenhouse, Box,and Huynh-Feldt corrected probability levels on the within-subject F tests are given along with theassociated test power.

Analysis of Variance Table

Source Sum of Mean Prob PowerTerm DF Squares Square F-Ratio Level (Alpha=0.05)A: Exercise 2 427.4445 213.7222 0.61 0.555040 0.076179B(A): Subject 15 5234.556 348.9704C: Time 2 547.4445 273.7222 36.92 0.000000* 0.999974AC 4 191.4444 47.86111 6.45 0.000716* 0.874052BC(A) 30 222.4444 7.414815

Probability Levels for F-Tests with Geisser-Greenhouse AdjustmentsGeisser HuynhGreenhouse Box Feldt

Regular Epsilon Epsilon EpsilonSource Prob Prob Prob ProbTerm DF F-Ratio Level Level Level LevelA: Exercise 2 0.61 0.555040B(A): Subject 15C: Time 2 36.92 0.000000* 0.000021* 0.000000* 0.000000*AC 4 6.45 0.000716* 0.009496* 0.000755* 0.000716*BC(A) 30

Power Values for F-Tests with Geisser-Greenhouse AdjustmentsGeisser HuynhGreenhouse Box Feldt

Regular Epsilon Epsilon EpsilonSource Power Power Power PowerTerm DF F-Ratio (Alpha=0.05) (Alpha=0.05) (Alpha=0.05) (Alpha=0.05)A: Exercise 2 0.61 0.076179B(A): Subject 15C: Time 2 36.92 0.999974 0.889537 0.999966 0.999974AC 4 6.45 0.874052 0.371111 0.867399 0.874052BC(A) 30

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• Analysis of variance• Box’s M test• Circularity test• Compound symmetry test• Contrasts• Covariance matrix tests• Epsilon values• F ratios

• Fixed or random factors• Geisser-Greenhouse• Huynh-Feldt correction• Mauchley’s test• Means plots• Multiple comparisons• Planned comparisons• Power values

• Probability levels• Randomized block designs• Repeated measures• Subject plots• Within-subject designs

Repeated Measures ANOVA

These programs can generate 2k factorial designs, B.I.B. designs, d-optimal designs, fractionalfactorial designs, Latin square designs, screening designs, Taguchi designs, and response surfacedesigns. NCSS also provides for the analysis of these designs using either the general purposeANOVA and regression procedures or specialized procedures for designs with factors at only twolevels.

Means and Effects Section

Term Term Estimated StandardNo. Symbol Mean - Mean + Effect Error0 Grand Mean 64.25 0.711 A (Temp) 52.75 75.75 23.00 1.412 B (Concentration) 66.75 61.75 -5.00 1.413 AB 63.50 65.00 1.50 1.414 C (Catalyst) 63.50 65.00 1.50 1.415 AC 59.25 69.25 10.00 1.416 BC 64.25 64.25 0.00 1.417 ABC 64.00 64.50 0.50 1.41

Analysis of Variance Section

Term Term Mean Prob StatisticallyNo. Symbol DF Square F-Ratio Level Significant1 A (Temp) 1 2116.0000 264.50 0.000000 Yes2 B (Concentration) 1 100.0000 12.50 0.007670 Yes3 AB 1 9.0000 1.13 0.319813 No4 C (Catalyst) 1 9.0000 1.13 0.319813 No5 AC 1 400.0000 50.00 0.000105 Yes6 BC 1 0.0000 0.00 1.000000 No7 ABC 1 1.0000 0.13 0.732810 No

Error 8 8.0000Total 15 2699.0000

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• Aliasing reports• Analysis of variance tables• Automatic design detection• Balanced incomplete block• Block confounding• Blocking• Box-Behnken designs• Box-Hunter-Hunter designs• Central composite designs• Contour plots

• D-optimal designs• Effect estimation• Fractional factorials• Latin Squares• Factorial designs• Means Plots• Placket-burman designs• Probability plots of residuals

and effects• Repeated Measures designs

• Residual analysis• Response-surface designs• Screening designs (up to 31

Factors)• Taguchi designs

Design of Experiments

Survival analysis includes several techniques to study data in which the response variable is elapsedtime. Procedures include survival distribution analysis (including the Kaplan-Meier survivaldistribution estimate), log rank tests, and proportional hazards regression.

Kaplan-Meier Product-Limit Survival Distribution

Sample Survivorship Std Error Hazard Fn Std ErrorRank Size Time S(t) of S(t) H(t)=-Log(S(t)) of H(t)1 19 3.0 .947368 .051228 .054067 .2389102 18 3.0+ 3 17 4.0 .891641 .072440 .114692 .3018554 16 6.0 .835913 .086738 .179230 .3523265 15 8.0 .780186 .097223 .248223 .3996576 14 8.0 .724458 .105043 .322331 .4473737 13 8.0+ 8 12 10.0 .664087 .112306 .409343 .5046349 11 12.0 .603715 .117205 .504653 .56707610 10 13.0+ 11 9 16.0 .536636 .121875 .622436 .65054712 8 17.0 .469556 .123732 .755967 .74912213 7 21.0+ 14 6 26.0+ 15 5 30.0 .375645 .129821 .979111 .95916916 4 33.0 .281734 .126865 1.266793 1.26424517 3 35.0+ 18 2 44.0+ 19 1 45.0+

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• Accelerated life testing• Beta distribution• Censoring – All Types• Cox’s regression• Cox-Mantel test• Exponential distribution• Exponential regression• Extreme Value distribution• Extreme Value regression• Gamma distribution• Gehan’s Wilcoxon test• Goodness of fit

• Hazard rate plots• Hazard functions & plots• Kaplan-Meier product limit• Least squares estimates• Log-logistic distribution• Log-logistic regression• Log rank test• Lognormal distribution• Lognormal regression• Maximum likelihood• Peto / Wilcoxon test• Probit Analysis

• Proportional hazardsregression

• Rayleigh distribution• Reliability statistics• Stress variables• Survival functions & plots• Survival percentiles• Variable selection options• Weibull distribution• Weibull regression

Survival Analysis

The reliability procedure estimates the parameters of the exponential, extreme value, logistic, log-logistic, lognormal, normal, and Weibull probability distributions by maximum likelihood and leastsquares. It can fit complete, right censored, left censored, interval censored (readout), and groupeddata values. It also computes the nonparametric Kaplan-Meier and Nelson-Aalen estimates ofreliability and associated hazard rates.

Another module fits the regression relationship between time-to-failure and one or moreindependent variables. The distribution of the residuals (errors) can follow the exponential, extremevalue, logistic, log-logistic, lognormal, lognormal10, normal, or Weibull distributions. The data mayinclude failed, left censored, right censored, and interval observations. This type of data often arisesin the area of accelerated life testing.

Weibull Parameter Estimation SectionProbability Maximum MLE MLE MLEPlot Likelihood Standard 95% Lower 95% Upper

Parameter Estimate Estimate Error Conf. Limit Conf. LimitShape 1.26829 1.511543 0.4128574 0.8849655 2.581753Scale 279.7478 238.3481 57.21616 148.8944 381.5444Log Likelihood -80.05649

Reliability SectionProb Prob Max Like 95% Lower 95% Upper

Failure Estimate of Estimate of Conf. Limit of Conf. Limit ofTime Survival Survival Survival Survival40.0 0.9186 0.9349 0.8065 0.979180.0 0.8151 0.8253 0.6728 0.9112120.0 0.7105 0.7016 0.5312 0.8199160.0 0.6112 0.5784 0.3775 0.7352

Percentile SectionProb Prob Max Like 95% Lower 95% Upper

Failure Estimate of Estimate of Conf. Limit of Conf. Limit ofTime Failure Failure Failure FailurePercentage Time Time Time Time25.0000 104.7 104.5 69.7 156.850.0000 209.5 187.0 124.7 280.575.0000 361.9 295.8 170.9 512.195.0000 664.5 492.6 227.8 1065.0

0.000

0.003

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Weibull Hazard Rate Plot

Time

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ard

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e

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4.75

5.50

-4.00 -3.13 -2.25 -1.38 -0.50

Weibull Probability Plot

Weibull Quantile

Ln(T

ime)

• Accelerated life testing• Arrhenius transformation• Beta distribution• Censoring – All Types• Confidence Limits• Cox-Snell Residuals• Distribution selection• Exponential distribution• Exponential regression• Extreme-value distribution• Extreme-value regression• Failure time percentiles

• Gamma distribution• Goodness of fit• Hazard rate plots• Hazard functions & plots• Information Matrix• Kaplan-Meier product limit• Least squares estimates• Log-logistic distribution• Log-logistic regression• Lognormal distribution• Lognormal regression• Maximum likelihood

• Probability plots• Reliability statistics• Residual Analysis• Residual Life Report• Stress variables• Stress plots• Threshold Estimate• Weibull distribution• Weibull regression

Reliability Analysis

NCSS provides a complete set of the latest variables and attribute control charts. It includes popularfeatures such as runs tests, individuals charts, automatic outlier removal, capability analysis, user-supplied sigma, and comprehensive chart labeling. Since the quality control programs are completelyintegrated with the rest of the system, once you detect an out-of-control signal, you can investigatewith the other procedures in NCSS.

Xbar and R Charts

1980

.019

88.8

1997

.520

06.3

2015

.0

0.0 30.0 60.0 90.0 120.0

Xbar Chart

Row

Xba

r

13 22 36

-10.

07.

525

.042

.560

.00.0 30.0 60.0 90.0 120.0

Range Chart

Row

Ran

ge

11

Out-of-Control ListRow Mean Range Row Label Reason4 6.8 5 4 Range: 4 of 5 in zone B or beyond5 12.2 48 5 Xbar: beyond control limits6 9.8 27 6 Xbar: 2 of 3 in zone A7 5.6 4 7 Xbar: 2 of 3 in zone A

Capability Analysis SectionParameter Lower Center Upper3-Sigma Limits -5.390758 6.036585 17.463934-Sigma Limits -9.199872 6.036585 21.27304Specification Limits 1 14Specification z-Values -1.322246 2.090621Percent Outside Specification 3.252033 2.439024Capacities 0.440749 0.696874Cp Index 0.518452 0.568811 0.619112Cpk Index 0.383108 0.440749 0.498389Count = 246 Sigma = 3.809114 Alpha Level = 0.050000

• Attribute charts• C chart• Capability analysis• Cp index• Cpk Index• Cusum chart• EWMA chart• Exception report• Frequency distribution• Histogram

• Individuals chart• Moving average chart• Moving range chart• Normality test• NP chart• Out-of-control list• P chart• Pareto charts• Primary control limits• R and R Study

• R chart• Robust chart analysis• Runs tests• S (sigma) chart• Secondary control limits• U chart• Variables charts• Xbar chart• Zone display

Quality Control Charts and SPC

Multivariate analysis refers to a group of statistical techniques that analyze two or more variables ata time, including: discriminant analysis, factor analysis, cluster analysis, logistic regression,MANOVA, and principal component analysis.

Factor Analysis ReportEigenvalues after Varimax Rotation

Individual CumulativeNo. Eigenvalue Percent Percent Scree Plot1 3.288191 54.89 54.89 |||||||||||2 2.701207 45.09 99.99 ||||||||||3 0.001207 0.02 100.00 |4 -.000099 0.00 100.00 |5 -.000121 0.00 100.00 |6 -.000295 0.00 100.00 |

Factor Loadings after Varimax RotationVariables Factor1 Factor2X1 -.019936 -.998792X2 -.967470 -.252572X3 -.994037 -.107126X4 -.478418 -.873578X5 -.594943 -.803812X6 -.883654 -.468080

-2.0

-0.8

0.5

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-2.0 -1.0 0.0 1.0 2.0

Factor Scores

Score2

Sco

re1

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3 4

567

8

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1112

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28 29

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Factor Loadings

Loading2

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ing1

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2 3

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6

• Discriminant Analysis• Canonical coefficient reports• Classification reports• Influential variable reports• Linear discriminant functions,

scores, and coefficients• Prior probabilities• Stepwise variable selection• Cluster Algorithms• Complete Linkage• Dendrograms• Fuzzy clustering• Hierarchical• K-means algorithm• Mediod partitioning• Nearest neighbor• Regression clustering• Single Linkage

• Factor and PrincipalComponent Analysis

• Bartlett’s sphericity test• Communality estimates• Correlation matrix input• Eigenvalue/vector analysis• Factor loadings and scores• Gleason-Staelin redundancy• Missing value estimation• Outlier detection• Principal axis method• Quartimax rotation• Robust estimation• Score and Loading Plots• Scree plot• T2 analysis• Varimax rotation• Equality of Covariance• Bartlett’s variance test• Box’s M test• Cronbachs alpha• Eigenvalue analysis

• MANOVA• Approximate F-test• Box’s M test• Canonical analysis• Homogeneity of variance test• Hotelling’s T2

• Lawley-Hotelling trace• Pillai’s trace• Roy’s largest root• Wilks’ lambda• Logistic Regression• Beta estimates• Chi-square tests• Classification table• Normal probability plots• Odds ratios• Predict new observations• Step-down variable selection• Step-up variable selection

Multivariate Analysis

Loglinear models techniques are used to analyze the relationships among the factors in a multi-waycontingency table. Several model selection techniques, goodness of fit tests, and parameterestimation reports are provided.

Correspondence analysis is a technique for graphically displaying a two-way contingency table bycalculating coordinates representing its rows and columns. These coordinates are analogous tofactors in a factor analysis.

Multidimensional scaling is a technique that creates a map displaying the relative positions of anumber of objects, given only a table of the distances between them. The program calculates eitherthe metric or the non-metric solution.

Loglinear Models Multiple-Term Test SectionLike. Ratio Prob Pearson Prob

K-Terms DF Chi-Square Level Chi-Square Level1WAY & Higher 31 2666.19 0.0000 3811.81 0.00002WAY & Higher 26 596.84 0.0000 751.31 0.00003WAY & Higher 16 19.56 0.2406 21.21 0.17054WAY & Higher 6 3.23 0.7791 3.32 0.76805WAY & Higher 1 1.02 0.3116 1.01 0.3157

Like. Ratio ProbK-Terms DF Chi-Square Level1WAY Only 5 2069.35 0.00002WAY Only 10 577.28 0.00003WAY Only 10 16.33 0.09064WAY Only 5 2.21 0.8196

-0.2

50.

15

-0.40 0.50

Correspondence Plot

Factor1 (88%)

Fac

tor2

(12%

)

SM

JM

SE

JESC

None

Light

Medium

Heavy

-1.5

0-0

.50

0.50

1.50

2.50

-4.00 -2.00 0.00 2.00 4.00

MDS Map

Dim1

Dim

2

Hockey

Football

Basketball

Tennis

Golf

Croquet

• Loglinear Models• Automatic model selection• Delta value for zero cells• Estimated effects• Goodness of fit statistics• Hierarchical models• Likelihood ratio tests• Pearson chi-square tests• Residual analysis• Up to seven factors

• Correspondence Analysis• Chi-square contributions• Column/row profiles• Coordinates report• Eigenvalues• Mass values• Point quality index• Supplementary rows• Variable/profile correlation

• Multidimensional Scaling• Classical (metric) scaling• Dissimilarity and correlation

input• Eigenvalue report• Kruskal’s stress statistic• Non-metric scaling

More Multivariate Procedures

NCSS provides several methods of forecasting and time series analysis. For forecasting, it providesclassical methods based on exponential smoothing, trend-season-cycle decomposition (like X11),and ARIMA (Box-Jenkins). For time series analysis, it provides spectral analysis, ARIMA, andautocorrelation analysis.

The program contains a theoretical procedure that generates univariate time series from a specifiedmodel. This is useful for improving your forecasting skills.

Model Estimation SectionParameter Parameter Standard ProbName Estimate Error T-Value LevelAR(1) 0.5778422 0.1725721 3.3484 0.000813AR(2) 0.3962256 0.1596349 2.4821 0.013062MA(1) 0.7604249 0.1349649 5.6342 0.000000Observations 40 Residual Sum of Squares 28.84119Iterations 20 Mean Square Error 0.7794916Pseudo R-Squared 21.586142 Root Mean Square 0.8828882

Autocorrelations of Residuals of Series1-MEANLag Correlation Lag Correlation Lag Correlation Lag Correlation1 -0.091919 11 0.003063 21 0.090220 31 0.0577362 -0.089101 12 0.000842 22 -0.036684 32 -0.0692543 -0.006732 13 -0.037963 23 0.105105 33 0.1122944 -0.091508 14 0.038344 24 0.048037 34 0.049954. . . . . . . .. . . . . . . .Significant if |Correlation|> 0.316228

-4.0

-2.5

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1990 2006 2022 2038 2054

Series1-MEAN Chart

Time

Ser

ies1

-ME

AN

-1.0

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.500

0.00

00.

500

1.00

0

0 10 19 29 38

Autocorrelations of Residuals

Lag

Aut

ocor

rela

tions

• ARIMA• ARMA• Autocorrelations• Automatic Box-Jenkins• Box-Jenkins Method• Census X11• Cycle Analysis• Decomposition Methods• Double-Exponential

Smoothing

• Easy To Use• Error Plots• Exponential Smoothing• Forecast Plots• Generate Series• Harmonic Analysis• Log Transformation• Modified Yule-Walker

Equations• Partial Autocorrelations

• Periodogram• Portmanteau Test• Prediction Limits - ARIMA• Residual Analysis• Seasonal Adjustment• Seasonal Analysis• Seasonal ARIMA Models• Spectral Analysis• Trend Analysis

Forecasting and Time Series Analysis

Qty___ NCSS 2000 CD and printed documentation: $399.95.......... $ ____

___ NCSS 2000 CD (electronic documentation): $299.95 ......... $ ____

___ PASS 2000 CD and Printed Manual: $249.95...................... $ ____

___ PASS 2000 Upgrade CD for PASS 6.0 users: $99.95............ $ ____

___ PASS 2000 Manual for PASS 6.0 users: $49.95 ................... $ ____

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Yes! I want to obtain the latest version of these NCSS products.Please rush me my own personal license of NCSS 2000 and/orPASS 2000 at their amazingly low prices.

HERE’S WHAT DR. BILL BIGG

OF HUMBOLDT STATE

UNIVERSITY FORESTRY

DEPARTMENT SAYS…

In the fifteen years I have beenteaching I have used severaldifferent statistical softwarepackages. None have beeneasier to learn and operate thanNCSS for Windows. The helpfile is particularly completeand makes interpretation of theoutput straight forward—evenwhen you can’t remember whata particular item means.

FOR FASTEST DELIVERY, CALL

1-800-898-6109Email your order to sales@ncss.comor fax your order to 1-801-546-3907

NCSS, 329 North 1000 East, Kaysville, UT 84037

HERE’S WHAT DR. CHET MCCALL OF

THE GRADUATE SCHOOL OF

EDUCATION AND PSYCHOLOGY AT

PEPPERDINE UNIVERSITY SAYS…

For more than seven years, we havewatched NCSS evolve into a mostuser friendly and powerful statisticalsystem. We find that NCSS is easyto use and, for those with a mathphobia, it does the job with minimalinstruction. Tutorials areoutstanding. Anybody in highereducation who needs statisticalsoftware could do well to viewNCSS. I personally feel it is the bestbuy on the market.

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HERE’S WHO’S PUBLISHING USING NCSS TO DO THEIR

ANALYSIS…

Am Heart Journal N.S. Kleiman 1994Am J. of Physical Anthropology C. Tardieu 1994Am J. of Physiology M. Okada 1994Analytical Biochemistry S. Butenas 1995Annals of Human Biology J.H. Relethford 1994Annals of Oncology L. Vanwarmerdam 1994Annals of Surgery J.A. Morris 1994Bone Marrow Transplantation E. Conde 1994Hypertension P. Boutouyrie 1995J. Am College of Nutrition M.J. Glade 1993J. Applied Physiology J. Qvist 1993J. of Family Practice R. Sheff 1994J. Pharmacy and Pharmacology P. Bustamante 1993Oecologia C.J. Bilbrough 1995Preventive Veterinary Medicine P.D. Mansell 1993

NCSS’S ACCURACY…We at NCSS have put a great deal of effort into finding the most accurate algorithms possible. Theprograms have been tested and verified over and over, both by us and by our customers. Each routine has been verified againsttextbooks, journal articles, and, where possible, other software. NCSS is one of the most accurate statistical analysis programsavailable. NCSS calculates with seventeen-digit, double-precision accuracy.

OUR GUARANTEE…If you are not completely satisfied with an NCSS product during the first 30 days for any reason, return the program for a full,prompt refund (excluding shipping)—no questions asked.

NOW YOU CAN…• Be up and running in less than 30

minutes with our Quick Startbooklet.

• Complete your first statisticalanalysis in less than an hour.

• Have your technical questionsanswered free by a PhD statistician.

• Have confidence when orderingbecause of our 30 day unconditionalmoney back guarantee.

NCSS LETS YOU…• Easily mix graphs and reports

together in a format recognized byword processors.

• Enter your data into a spreadsheet.• Have confidence in the accuracy of

your results since they are backedby our 18-year-old company.

• Spend your time doinginterpretation rather thanprogramming.

• Analyze large (200,000+ rows)

WHEN YOU BUY NCSS, YOU WILLHAVE A PROGRAM THAT…• Is comprehensive and accurate• Is easy to learn and use.• Imports and Exports all major spreadsheet,

database, and statistical file formats (includingExcel and dBase).

• Outputs reports in a tabbed format that is readyfor Word or Word Perfect.

• Costs least than half what our competitorscharge.